Dielectric Permittivity

Dielectric permittivity (ε) is grounded in complex physics but in simple terms it can be described as the ability of a substance to hold an electrical charge.

The dielectric constant (Ka) is the ratio of the permittivity of a substance to free space. The value of Ka in air is 1 and in water Ka is approximately 80.

Many materials have an ε or Ka. For example, the Ka of glass is between 5 and 10, the Ka of paper is between 2 and 4, and the Ka of body tissue is approximately 8.

The behavior of electromagnetic waves from 1 to 1000 MHz in soil can be used to measure or characterize the complex dielectric permittivity. Dielectric permittivity was first mathematically quantified by Maxwell’s Equations in 1870s. In 1980, G. C. Topp proposed a method and a calibration to predict soil moisture based on the electrical properties of the soil known as the Topp Equation. Today, the many different kinds of soil moisture sensors commercially available in one way or another base their soil moisture estimation on the dielectric permittivity.

Among all of the electronic soil sensors commercially available, measurement involving the complex dielectric permittivity remains the most practical way to determine soil water content from an in-situ sensor or portable device. Electromagnetic soil sensors use an oscillating radio frequency and the resultant signal is related to the dielectric permittivity of the soil where the in-situ soil particle/water/air matrix is the dielectric. Subsequent calibrations then take the raw sensor response to a soil moisture estimation.

The Ka of water varies slightly with temperature and pressure. A Ka value of 80 assumes water is at room temperature. Owen et al (1961) cite Ka values for water across a range of temperature and pressure. There is an inverse relationship between temperature and the Ka of water, where Ka decreases with increasing temperature.

The temperature dependency of water’s Ka has significant implications for the calibration of soil water content sensors. Typically, calibration of sensors is conducted at room temperature. However, soil temperature in the field can vary from extremely low to very high. Most researchers, and certainly most growers, ignore the effects of temperature on Ka when reporting soil water content values. Other variables, particularly soil electrical conductivity, can compound the effects of temperature on the accuracy of soil water content sensors.

Dielectric Theory

Complex dielectric permittivity describes a material’s ability to permit an electric field. As an electromagnetic wave propagates through matter, the oscillation of the electric field is perpendicular to the oscillation of the magnetic field and these oscillations are perpendicular to the direction of propagation. The dielectric permittivity of a material is a complex number containing both real and imaginary components and is dependent on frequency, temperature, and the properties of the material. This can be expressed by:

K asterisk times equals epsilon subscript r minus j epsilon subscript i

[1]

where К* is complex dialectic permittivity, εr is the real dielectric permittivity, εi is the imaginary dielectric permittivity and j equals square root of negative 1 end root (Topp 1980).

As the radio wave propagates and reflects through soil, the properties and water content of the soil will influence the wave. The water content, and to a lesser extent the soil properties will alter and modulate electromagnetic radio signals as they travel through the soil by changing the frequency, amplitude, impedance and the time of travel.

The dielectric permittivity can be determined by measuring these modulations to the radio frequency as it propagates through the soil. In general, the real component represents energy storage in the form of rotational or orientation polarization which is indicative of soil water content. The real dielectric constant of water is 78.54 at 25°C and the real dielectric permittivity of dry soil is typically about 4. Changes in the real dielectric permittivity are directly related to changes in the water content and all electromagnetic soil sensors base their moisture calibrations on either a measurement or estimation of the real dielectric permittivity of the soil particle/water/air matrix. (Jones 2005, Blonquist 2005). The imaginary component of the dielectric permittivity:

epsilon subscript i equals epsilon subscript r e l end subscript plus fraction numerator sigma subscript d c end subscript over denominator 2 pi ⨍ epsilon subscript v end fraction

[2]

represents the energy loss where εrel is the molecular relaxation, ⨍ is the frequency, εv permittivity of a vacuum, and σdc is DC electrical conductivity. In most soils, εrel is relatively small and a measurement of the imaginary component yields a good estimation of the electrical conductivity from 1 to 75 MHz (Hilhorst 2000). In sandy soils, the molecular relaxation can be negligible.

The storage of electrical charge is capacitance in Farads and is related to the real component (non-frequency dependent) by:

straight C equals gε space straight epsilon subscript straight v

[3]

Where g is a geometric factor and ε is the dielectric constant. If the electric field of the capacitor is oscillating (i.e. electromagnetic wave), the capacitance also becomes a complex number and can be describe in a similar fashion as the complex dielectric permittivity in equations [1] and [2] (Kelleners 2004).

The apparent dielectric permittivity εa, is a parameter that contains both the real and the imagery dielectric permittivities and is the parameter used by most soil sensors to estimate soil moisture.

straight epsilon subscript straight a equals left curly bracket 1 plus left square bracket 1 plus tan squared left parenthesis straight epsilon subscript straight i divided by straight epsilon subscript straight r right parenthesis right square bracket to the power of 1 divided by 2 end exponent right curly bracket straight epsilon subscript straight r divided by 2

[4]

From equation [4], the apparent dielectric permittivity is a function of both real and imaginary components (Logsdon 2005). High values of εi will inflate the εa which may cause errors in the estimation of soil moisture content. In an attempt to shrink the errors in the moisture calibration from the εi, some soil sensor technologies such as time domain reflectometry (TDR) and time domain transmissometry (TDT) will operate at high frequencies giving the εa more real character. In practice, soils high in salt content will inflate the soil moisture measurement because εa will increase due to the DC conductivity component of εi. Also, the εi is much more sensitive to temperature changes than εr, creating diurnal temperature drifts in the soil moisture data (Blonquist 2005, Seyfried 2007). Soil moisture sensors that can best isolate the real component and delineate it from the imaginary will be the most accurate and will have a lower inter-sensor variability.

Water is a polar molecule, meaning that one part of the water molecule carries a negative charge while the other half of the molecule carries a positive charge. While water is very polar, soils are rather non-polar. The polarity of water causes a rotational dipole moment in the presence of an electromagnetic wave while soil remains mostly uninfluenced.

1. Terminology note. The term “real dielectric constant” generally refers to a physical property that is constant at a specified condition. The term “real dielectric permittivity” or “real permittivity” refers to the real dielectric constant of a media that is undergoing change, such as soil.

This means that water will rotate and reorientate with the rise and fall of the oscillating electric field (i.e. the electromagnetic wave) while soil remains mostly stationary. From 1 to 1000 MHz, the water rotational dipole moment will occur at the same frequency of the electromagnetic wave. It is this rotational dipole moment of water that is responsible for water’s high dielectric constant1 of about 80. Large changes in the dielectric permittivity are directly correlated to changes in soil moisture.

A water molecule in the liquid phase reorienting i.e. rotational dipole moment.

Illustration of polarization. The real dielectric permittivity of soil is mostly due to orientation polarization of water (Taken from Lee et al. 2003)

How Temperature Affects Dielectric Permittivity

Both the real and imaginary dielectric permittivities will be influenced by temperature. The imaginary component is much more sensitive to changes in temperature than the real component. (Seyfried 2007).

The real dielectric permittivity of water will have a slight dependence on temperature. As the temperature increases, molecular vibrations will increase. These molecular vibrations will impede the rotational dipole moment of liquid water in the presence of an oscillating electric field; consequently, the real dielectric permittivity of water will decrease as the temperature increases. The empirical relationship with temperature found in the literature is shown in equation [5] (Jones 2005):

straight epsilon subscript straight r comma straight w end subscript left parenthesis straight T right parenthesis equals 78.54 left square bracket 1 minus 4.579 straight X 10 to the power of negative 3 end exponent left parenthesis straight T minus 298 right parenthesis plus 1.19 straight X 10 to the power of negative 5 end exponent left parenthesis straight T minus 298 right parenthesis squared minus 2.8 straight X 10 to the power of negative 8 end exponent left parenthesis straight T minus 298 right parenthesis cubed right square bracket

[5]

The dielectric constant of water in liquid form decreases with increasing temperature, but in soil, water’s dielectric dependence on temperature is more complicated due to bound water effects. As temperature changes, the molecular vibrations of the water and cations (positive ions) that are bonded to soil particles at a microscopic level can affect the dipole moments in the presence of a radio frequency. In practical terms, temperature correction to soil moisture calibrations are highly soil-dependent. In some soils, the real dielectric can trend downward with increasing temperature as it does in liquid form, or it can trend upward with increasing temperature (Seyfried 2007).

The imaginary permittivity is highly temperature-dependent and that dependence is similar to that of the bulk electrical conductivity.

Measuring Apparent vs. Imaginary Dielectric Permittivity

Most soil sensors measure the apparent dielectric permittivity by making an assumption of the imaginary permittivity. That is, the apparent dielectric permittivity measurement mixed together the real and imaginary permittivity (Logsdon 2010). Such a mixed measurement is prone to error since soil is not all about water. Other variables such as salinity, temperature, conductivity, and mineralogy can independently influence the real and the imaginary permittivity. Errors can occur when such variables are not independently characterized in measuring the real and the imaginary permittivity. The “real dielectric” represents water alone. The “imaginary dielectric” represents the other things that are not related to water.

The variability of soil properties in space, time, and geographical location presents a challenge for each site assessment and the detection of changes in soil conditions within and among sites. Spatial variations include horizontal variations across a landscape and vertical variations with horizon depth. These variabilities are due to numerous factors including mineralogy, animal/insect activity, windthrow, litter and wood inputs, human activity, plants, precipitation chemistry, tillage, compaction, seasonality, etc. These soil variables have an impact on the apparent dielectric permittivity.

Most sensors based on universal standards (such as NIST traceable standards) do not have such changing site-specific variables, and make assumptions about the imaginary dielectric permittivity (which are impacted by such variables).  For the highest accuracy, sensors should base the soil moisture calibration on the real dielectric permittivity only. 

Only one sensor technology—Coaxial Impedance Dielectric Reflectometry—measures both the real and the imaginary components of the dielectric permittivity as separate parameters. Basing the soil moisture calibration on the real dielectric permittivity instead of the apparent permittivity has several advantages: soil moisture calibrations are less affected by soil salinity, temperature, soil variability and inter-sensor variability.

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